A road information acquisition unit (12a) acquires information about the road in a prescribed segment in front, a vehicle information acquisition unit (12b) acquires information about the vehicle (1), a velocity prediction unit (12c) predicts, on the basis of the road information and the information about the vehicle (1), the changes in the vehicle velocity that would be brought about in the prescribed segment in the case of travelling the prescribed segment in a first gear, and a shift control unit (12d) which maintains the first gear if the condition is satisfied that the predicted vehicle velocity exhibits a minimum value other than at the ends of the prescribed segment and the minimum value is greater than the delay speed, which is set to a value less than a predetermined velocity set as the velocity that would result from downshifting.